The Structure of an Outbreak on a College Campus

Document Type

Article

Publication Title

Mathematics Magazine

Department

Mathematics

ISSN

0025-570X

Volume

94

Issue

2

DOI

10.1080/0025570X.2021.1867450

First Page

83

Last Page

98

Publication Date

1-1-2021

Abstract

We provide a brief introduction to a class of flexible random graph SIR models that allow for a random number of connections per student and are relatively easy to simulate. We present an application of these individual-based models to study a seasonal outbreak of influenza at our home institution. Using data obtained from a survey of students, we find that the right skewed beta negative binomial distribution provides a good fit to the degree distribution of student contacts with a mean of about 25 contacts per student. With no vaccinations or change in student behavior, our model predicts that a highly contagious influenza virus would spread to about 90% of the student body while even a less virulent strain would infect about one-half of the population. Our investigations conclude with an exploration of targeted vs random vaccination strategies. Individual based random graphs models not only provide exciting opportunities for undergraduate research, but provide insights into the structure of epidemics on college campuses.

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